Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,4) and (−8,8)

y=−1/5x+2

Step-by-step explanation:

First, you must find the midpoint of the segment, the formula for which is

(x1+x22,y1+y22)

. This gives (−5,3)

as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula

y2−y1x2−x1

which gives us a slope of 5

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of

5 is −1/5

We now know that the perpendicular travels through the point (−5,3)

and has a slope of −1/5

Solve for the unknown b in y=mx+b

3=−1/5(−5)+b⇒3=1+b⇒2=b

Therefore, the equation of the perpendicular bisector is

y=−1/5x+2

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.